Find the probability of each event. (Reduce all fractions to simplest form)

a. Rolling a number that is a factor of 6 on a standard number cube

b. Drawing a purple cube from a bag of 15 cubes, 5 of which are purple.

c. Drawing a king from a standard deck of 52 cards.

d. Drawing an eight or nine of hearts from a standard deck of 52 cards.

Part (a)

Work Shown:

There are 6 numbers on the die total, 4 of which are factors of 6 (1,2,3,6)

So 4/6 = 2/3 is the answer.

Part (b)

Work Shown:

There are 5 purple cubes out of 15 total

5/15 = 1/3

Part (c)

Work Shown:

There are 52 cards, 4 of which are kings (one of each suit)

4/52 = 1/13 is the probability of getting a king

we do not include joker cards

Part (d)

Work Shown:

E = event space

E = {8H, 9H} there are two items in the event space

The notation "8H" means "8 of hearts".

S = sample space

S = set of 52 cards

Divide the number of items in set E over the number of items in set S

2/52 = 1/26

Again we do not include joker cards.

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

7.3

step-by-step explanation: